I have no idea if the heater helps keeping the water from going bad, for us it's to get the water temp to the proper level for top-off use and also when running the water into the RODI salt, helps dissolve the salt faster.
Powerheads in the tank is to keep the water from becoming stagnant like you mentioned. We could be completely wrong, but this has worked for us and the TDS hasn't changed from 0.